Leo T. Butler

Magnetic Flows on Sol-Manifolds: Dynamical and Symplectic Aspects

We consider magnetic flows on compact quotients of the 3-dimensional solvable geometry Sol determined by the usual left-invariant metric and the distinguished monopole. We show that these flows have positive Liouville entropy and therefore are never completely integrable. This should be compared with the known fact that the underlying geodesic flow is completely integrable in spite of having positive topological entropy. We also show that for a large class of twisted cotangent bundles of solvable manifolds every compact set is displaceable.

THE MASLOV COCYCLE, SMOOTH STRUCTURES, AND REAL-ANALYTIC COMPLETE INTEGRABILITY

This paper proves two main results. First, it is shown that if

An optical Hamiltonian and obstructions to integrability

\Sigma

Positive-entropy Hamiltonian systems on Nilmanifolds via scattering

is a smooth manifold homeomorphic to the standard

Positive-entropy integrable systems and the Toda lattice, II

n

Positive-entropy geodesic flows on nilmanifolds

-torus

Invariant tori for the Nosé thermostat near the high-temperature limit

{\bf T}^n = {\bf R}^n/{\bf Z}^n

Smooth Structures on Eschenburg Spaces: Numerical Computations

and

A Bayesian approach to the estimation of maps between Riemannian manifolds

H

A Bayesian Approach to the Estimation of Maps between Riemannian Manifolds. II: Examples

is a real-analytically completely integrable convex hamiltonian on